The spin–orbit coupling induced stereochemical activity and nonlinear optical response in Pb2BO3X (X = Cl, Br, I)

Abstract

Spin-orbit coupling (SOC) has gained significant attention for its ability to modify electronic structures and optical properties. In this study, first-principles calculations are employed to investigate the electronic structures and optical properties of Pb₂BO₃X (X = Cl, Br, I) induced by SOC. The results reveal that SOC induces band downshifting and splitting at the top of the valence band (VB) and the bottom of conduction band (CB), leading to decreasement of GGA-PBE and HSE06 bandgaps. The GGA-PBE bandgaps of Pb₂BO₃X (X = Cl, Br, I) decrease from 3.55, 3.33, and 3.00 eV to 3.42, 3.11, and 2.70 eV, respectively, and the reduced HSE06 bandgaps (4.27, 3.88, and 3.50 eV for Pb₂BO₃Cl, Pb₂BO₃Br, and Pb₂BO₃I) are closer to experimental values. It is also observed that the stereochemical activity of lone pairs around the Pb atoms is enhanced with the inclusion of SOC. Furthermore, SOC leads to attenuated second harmonic generation (SHG) coefficients for Pb₂BO₃X (X = Cl, Br, I), with values of 9.00, 10.00, 11.34 × KDP (KH₂PO₄), which are in closer agreement with experimental values. Using the “shifting of conduction band” method, we find that the band splitting and downshifting induced by SOC contribute to a reduction in the effective SHG response. These findings provide valuable insights into the role of SOC in tuning the electronic and optical properties of Pb₂BO₃X (X = Cl, Br, I), offering potential pathways for designing materials with enhanced nonlinear optical responses.